Problem: Solve for $x$ and $y$ using elimination. ${5x+y = 19}$ ${3x+2y = 24}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-10x-2y = -38}$ $3x+2y = 24$ Add the top and bottom equations together. $-7x = -14$ $\dfrac{-7x}{{-7}} = \dfrac{-14}{{-7}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {5x+y = 19}\thinspace$ to find $y$ ${5}{(2)}{ + y = 19}$ $10+y = 19$ $10{-10} + y = 19{-10}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {3x+2y = 24}\thinspace$ and get the same answer for $y$ : ${3}{(2)}{ + 2y = 24}$ ${y = 9}$